Demographic determinants of biometric heritability

Abstract

The response of quantitative characters to selection depends on their transmission from parents to offspring. A common estimate of this transmission is the biometric heritability defined as the slope of the regression of offspring phenotype on same-aged mid-parent phenotype (i.e. the ratio of the phenotypic parent-offspring covariance over the parental phenotypic variance). This slope is often interpreted as the percentage of phenotypic variation due to additive genetic effects after accounting for confounding factors such as environment, litter or parental effects. However, researchers seldom account for the possible influence of selection on this estimate. Here we study the effect on biometric heritability of fertility and viability selection, as well as phenotype ontogeny (growth) and inheritance from parents to offspring. We present exact formulas for the elasticities of biometric heritability in age-phenotype-structured integral projection models (IPMs), and illustrate these for two iteroparous long-lived species. We find that both viability and fertility selection can strongly affect heritability, mediated by growth and inheritance. Generally, demographic processes that result in parents reproducing at large phenotypes, regardless of their own birth phenotype, decrease heritability. Analysed at equilibrium, our models imply that a heritable character can show no response to selection, if parental phenotypes affect offspring phenotypes and if phenotypes develop with age. Our results further highlight the importance of accounting for demographic processes when estimating heritability.